An order of magnitude is an approximation of the logarithm of a value relative to some contextually understood reference value ten, interpreted as the base of the logarithm and the representative of values of magnitude one. Logarithmic distributions are common in nature and considering the order of magnitude of values sampled from such a distribution can be more intuitive; when the reference value is ten the order of magnitude can be understood as the number of digits in the base-10 representation of the value. If the reference value is one of certain powers of two, the magnitude can be understood as the amount of computer memory needed to store the exact integer value. Differences in order of magnitude can be measured on a base-10 logarithmic scale in “decades”. Examples of numbers of different magnitudes can be found at Orders of magnitude; the order of magnitude of a number is the smallest power of 10 used to represent that number. To work out the order of magnitude of a number N, the number is first expressed in the following form: N = a × 10 b where 1 10 ≤ a < 10.

B represents the order of magnitude of the number. The order of magnitude can be any integer; the table below enumerates the order of magnitude of some numbers in light of this definition: The geometric mean of 10 b and 10 b + 1 is 10 × 10 b, meaning that a value of 10 b represents a geometric "halfway point" within the range of possible values of a. Some use a simpler definition where 0.5 < a ≤ 5 because the arithmetic mean of 10 b and 10 b + c approaches 5 × 10 b + c − 1 for increasing c. This definition has the effect of lowering the values of b slightly: Yet others restrict a to values where 1 ≤ a < 10, making the order of magnitude of a number equal to its exponent part in scientific notation. Orders of magnitude are used to make approximate comparisons. If numbers differ by one order of magnitude, x is about ten times different in quantity than y. If values differ by two orders of magnitude, they differ by a factor of about 100. Two numbers of the same order of magnitude have the same scale: the larger value is less than ten times the smaller value.

The order of magnitude of a number is, intuitively speaking, the number of powers of 10 contained in the number. More the order of magnitude of a number can be defined in terms of the common logarithm as the integer part of the logarithm, obtained by truncation. For example, the number 4000000 has a logarithm of 6.602. When truncating, a number of this order of magnitude is between 106 and 107. In a similar example, with the phrase "He had a seven-figure income", the order of magnitude is the number of figures minus one, so it is easily determined without a calculator to 6. An order of magnitude is an approximate position on a logarithmic scale. An order-of-magnitude estimate of a variable, whose precise value is unknown, is an estimate rounded to the nearest power of ten. For example, an order-of-magnitude estimate for a variable between about 3 billion and 30 billion is 10 billion. To round a number to its nearest order of magnitude, one rounds its logarithm to the nearest integer, thus 4000000, which has a logarithm of 6.602, has 7 as its nearest order of magnitude, because "nearest" implies rounding rather than truncation.

For a number written in scientific notation, this logarithmic rounding scale requires rounding up to the next power of ten when the multiplier is greater than the square root of ten. For example, the nearest order of magnitude for 1.7×108 is 8, whereas the nearest order of magnitude for 3.7×108 is 9. An order-of-magnitude estimate is sometimes called a zeroth order approximation. An order-of-magnitude difference between two values is a factor of 10. For example, the mass of the planet Saturn is 95 times that of Earth, so Saturn is two orders of magnitude more massive than Earth. Order-of-magnitude differences are called decades. Other orders of magnitude may be calculated using bases other than 10; the ancient Greeks ranked the nighttime brightness of celestial bodies by 6 levels in which each level was the fifth root of one hundred as bright as the nearest weaker level of brightness, thus the brightest level being 5 orders of magnitude brighter than the weakest indicates that it is 5 or a factor of 100 times brighter.

The different decimal numeral systems of the world use a larger base to better envision the size of the number, have created names for the powers of this larg

Jaco Fourie is a South African equestrian athlete and SA National Champion in dressage. He lives near South Africa in the Northern Cape, on a Kalahari farm, he appeared on the cover of the May 2007 edition of the SA Horseman Magazine. Since 2009 he is married to Magda Fourie and together they have 2 daughters "Hanneke & Adelinde Fourie" and a son "Andrè Fourie"; the couple own & Dressage Academy. Jaco Fourie started his riding career in the family business of his father and 2 brothers at the age of 4, was tutored and mentored by many riding professionals to young adulthood, he had training from bereiters and instructors from the Spanish Riding School in Vienna, the SA Lipizzaner Centre, Natalie Hobday and Jonny Hilberath. His first Free State Provincial Colours were awarded in 2003, received his National Protea Colours for dressage in 2007. Fourie has represented his home-country, South Africa in the Equestrian Tri-Nations Competition on two occasions in 2007 and 2008 in Hawke's Bay, New Zealand.

He won the SA Championships in 2006, 2007 and 2008. He won the FEI World Dressage Challenge in 2005, he is the leading South African rider in the South African National Equestrian Federation's dressage rankings. He worked full-time as stud manager for CALLAHO Warmblood Sport Horses, a South African based horse breeding stud farm, a major sponsor of international riders, but has since moved onto his own property where he owns & manages Areion Warmblood Horses & Dressage Academy, his first pony was a crossbred Welsh pony named Prins. In dressage, Fourie rode CALLAHO's For Joy, CALLAHO's Granulit, CALLAHO's Rosengirl, CALLAHO's Benicio and AREION's Deja Vu to National honours. However, he had various other successes with horses FD Ref's Asterix, Etherow Impasse, BrandenburgSuper C, Alzu Catapault, Kehilan Shaheer and Kingsdale Kildaire amongst others. CALLAHO Warmblood Sport Horses South African National Equestrian Federation Free State & Northern Cape Horse Society Areion Warmblood Horses & Dressage Academy

Domenico Gilardi, was an Italian architect who worked in Moscow, Russia in Neoclassicist style. He was one of key architects charged with rebuilding the city after the Fire of 1812. Gilardi’s legacy survives in public buildings like Moscow Orphanage, Widows’ House, Catherine’s Institute and the Old Hall of Moscow University; the Gilardi family of architects from Ticino, established itself in Russia in the middle of the 18th century. Domenico’s father Giovanni known as Ivan Dementievich, was well known in Moscow. Domenico was born in Montagnola and lived there until his mother brought him to Russia in 1796. Domenico longed for a career in painting, so in 1799, his father sent him to an Italian workshop in St. Petersburg. After the death of Paul I, dowager Empress Maria Feodorovna awarded him a scholarship, a state-financed study tour to Italy. From 1803-1810 Domenico studied art in Milano, Florence and Rome. Domenico returned to Russia in June 1810, in January 1811 joined his father, the architect of the enormous Moscow Orphanage.

The first two stages of this enormous structure, conceived by educator Ivan Betzkoy, were completed in 1764-1781 and required continuous additions and improvements. Domenico remained in the employ of the Orphanage for the rest of his career. In 1812, after the Battle of Borodino, Gilardis fled Moscow; the city burnt down in September 1812. In 1813, Domenico joined the Kremlin Building Commission, restoring Ivan the Great Bell Tower and other war losses. In 1817, his father returned to Ticino. In 1817-1819 he completed his first independent job, reconstruction of Matvei Kazakov’s University in Mokhovaya Street. Gilardi retained the basic floorplan, but changed exterior styling. In 1818, he received commissions to rebuild the Widows’ House and Catherine’s Institute. In a short time, Gilardi concentrated the efforts to restore the four largest public buildings in the city, with the aid of Afanasy Grigoriev, a emancipated serf architect. Gilardi's style goes back to the Milano variety of Empire Classicism, Luigi Cagnola and in particular Antonio Antolini's Bonaparte Forum.

Grigoriev followed the same canon. Gilardi's architectural talent is disputed, but his success in construction management and ability to lead concurrent major projects is unquestionable, his first work in new construction was the Board of Trustees building, a new block on the Orphanage lot. It was followed by private commissions from the Golitsyn families. In 1826-1832, Gilardi supervised the rebuilding of Slobodskoy Palace in Lefortovo, a subsidiary of the Orphanage. Grigoriev replaced his. After less than twenty years of active practice, Gilardi retired and left for Switzerland in 1832. Back home, he completed only one project – a chapel near Montagnola. Giliardi's students and junior partners continued work in Moscow: Afanasy Grigoriev Alessandro Gilardi Yevgraph Tyurin New Construction 1814-1822 Lunin House 1820-1822 Gagarin House 1820-1832 Kuzminki Estate: Riding Court, Services 1823-1826 Trustees House at The Orphanage 1829-1831 Usachev House Reconstruction 1813-1817 - Kremlin: assistant architect for Ivan the Great bell tower 1817-1819 - Moscow University 1818-1824 - Catherine's Institute 1818-1823 - Widow's House 1826-1832 - Slobodskoy Palace